Existence of the Positive Solutions for some Boundary Singularity Elliptic Equation with Critical Sobolev-Hardy Exponent

In this paper, we consider the existence of the positive solutions for some semi-linear elliptic equations involving crtical Sobolev-Hardy exponent.This problem has boundary singularities (0 ∈∂Ω). Using variational methods and the strong maximum principle, we get the existence of a positive solution and generalize the existing results.